Algebraic Analysis

Duration

30h Th, 10h Pr, 20h Mon. WS

Number of credits

Lecturer

Jean-Pierre Schneiders

Language(s) of instruction

French language

Organisation and examination

Teaching in the second semester

Schedule

Schedule online

Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

Learning unit contents

This course presents first the basic results of the theory of sheaves and then deals with the theory of modules over the sheaf of linear differential operators with holomorphic coefficients. One then shows how the study of these modules is related to the one of systems of partial differential equations in the complex domain. Finally, one shows how to apply some results of homological algebra and sheaf theory to obtain local and global informations on the solutions of systems of this kind.

Learning outcomes of the learning unit

At the end of the course, the students should be able to understand recent works on algebraic analysis and to begin a research work in this field.

Prerequisite knowledge and skills

Good knowledge of algebra, topology, geometry, analysis and of algebraic topology.

Planned learning activities and teaching methods

The course consists of blackboard lessons, exercises sessions and a personal work.
During the lessons, the main theoretical results are introduced, established and illustrated with examples.
During the exercises sessions, the students are trained to solve by themselves various problems using the results considered in the lessons
The personal work consists of the preparation of a short paper presenting and establishing a result related to the course but not considered during the lessons.

Mode of delivery (face-to-face ; distance-learning)

Face-to-face course.

Recommended or required readings

Reference texts are pointed out at the beginning of the course.

Assessment methods and criteria

An examination comprising an oral part on the theory and a presentation of the personal work is organized during the first session. A similar examination is organized during the second session.

Work placement(s)

Organizational remarks

The course follows the official schedule handed out to the students at the beginning of the academic year.

Contacts

Jean-Pierre Schneiders Département de Mathématique (Bât. B37, Bureau 1/60) Allée de la Découverte, 12 - 4000 Liège (Sart-Tilman) Phone: (04) 366.94.01 - E-Mail: jpschneiders@ulg.ac.be Web page: http://www.analg.ulg.ac.be/jps/

Items online